Probably the latter. I've read more than one Ottoman report of armoury officials complaining about musketmen (not all Ottoman musketmen were Janissaries, mind you, and even if so, by the time firearms became commonplace in the hands of Ottoman soldiers, the Janissaries were no longer the elite that Westerners know them as) selling their state-issued musket off to Anatolia (where it went to rebel hands), and using that money to get themselves custom, embellished guns. State-issue muskets were not well liked by troops, but whether they had reason to complain about its quality or were just showing signs of praetorian hubris is up for debate.
That, and the Ottoman musket never evolved as the European musket did, so most matchlock examples were probably easily converted to miquelets at some point, with no change to the stock other than the attachment of the new lock. The Royal Armouries in Leeds, England, and either the State Hermitage Museum or the Kremlin Museum in Russia have examples of less embellished Ottoman muskets, and honestly, they don't look like much, save their barrels: